Mr Corbyn said he had tabled the emergency debate motion on the Brexit vote process, adding: 'We have no confidence in this Government'.
Senior party figures would not be drawn on whether Labour would table a motion of no-confidence in the Government after the vote, indicating they would wait and see what happens in the aftermath of a Government defeat on such a defining policy issue.
"It's clear the Prime Minister can't command confidence in Parliament", said the Labour backbencher.
The Prime Minister's official spokesman said Mrs May would observe the "spirit" of the EU Withdrawal Act, which requires the Prime Minister to make a statement to the Commons "before the end of 21 January" if no agreement in principle has been reached with Brussels.
Conservative MP Anna Soubry challenged Mr Corbyn to bring a motion of no confidence in her own government, saying: "The biggest obstacle to a People's Vote at the moment is Jeremy Corbyn".
Green MP Caroline Lucas appealed to Mr Corbyn as a "friend and a colleague" who shared her desire for "radical" change to the country.
There have been calls among MPs to move a motion of no confidence in the Prime Minister.
Mrs May later added she has "made some progress" and said there are still "discussions to be held".
She told BBC's Andrew Marr Show: "Once the deal falls, the Prime Minister is under a duty then to set out what she is going to do next". No more delays, no more tricks, let Parliament take control.
Roberts, says there is an "overwhelming" case for a confidence motion following Mrs May's decision to defer the crunch Commons vote on her Brexit deal. "Whatever happens with her Conservative leadership vote today, it is utterly irrelevant to the lives of people across our nation, and it does nothing resolve the government's inability to get a deal that works for the whole country".
And she called on European Union leaders to begin discussions at their summit on Thursday to extend Article 50 - the legal mechanism taking the UK out of the European Union on 29 March - to give the UK Parliament the "time and space" to explore the option of deciding to stay in.
Mrs May attempted a joke which played on the name of shadow global trade secretary Barry Gardiner, labelling him the "inconstant Gardiner", before adding: "Can I say to (Mr Corbyn) that he should be honest with people about his position - he couldn't care less about Brexit".
He said: "We should be having the vote and it should be happening next week".
The government tried to unilaterally pull that and deny this house the chance of a vote on this crucial matter.
"The Prime Minister is in a bunker".